To add to what Roger gave you, here's a link to the Catholic parish records for Bekan which are available online, which appear to go back to the 1820's for marriages and the 1830's for baptisms:
https://registers.nli.ie/parishes/1050
and here's a link to a site with other records for Bekan (in Irish, Béacán), which lists the 63 townlands (smaller geographic divisions) within the parish:
https://www.townlands.ie/mayo/bekan2/
The map at that site shows the boundaries of the civil parish of Bekan. Civil parish boundaries are not always the same as those for the local Catholic parish, but in this case the boundaries are the same for both. As you can see from the list there, Island (in Irish: An tOileán) is one of those townlands, and here is a link to the page specifically about Island:
https://www.townlands.ie/mayo/costello/bekan/bekan/island/
If you have access to Google Earth, you can also see an aerial view of Island there by searching for "Island, Bekan, Mayo"
The Barrett’s, by the way, were an Anglo-Norman family which settled in Ireland in the 12th and 13th centuries, where they became fully Hibernicized. Two different branches of the family existed. The branch which settled in Mayo mostly Hibernicized their name as Bairéid, and the related branch in County Cork used the form Baróid. One part of the Mayo Barrett's later assumed the surname Mac Aindriu (anglicized as McAndrew). They settled in an area not too far north of Bekan, on the east side of Lough Conn, and my own McAndrew ancestors lived near there, so I suppose we are distant cousins.